Consider the numbers 376, 438, 476, 389 and 567. In each number, the first and second digits are to be interchanged (for example, ABC becomes BAC). After this interchange, the resulting numbers are arranged in descending order. Which original number will then occupy the second position in this descending list?

Introduction / Context:
This problem combines number manipulation with ordering. The numbers given must first be transformed by swapping their first two digits, and only then should they be arranged in descending order. The question asks which original number will occupy the second place in the descending list after this transformation, so we must track both the changed values and their original identities.

Given Data / Assumptions:

• The original numbers are 376, 438, 476, 389, and 567.
• For each number ABC, we interchange the first two digits to form BAC.
• After transformation, we arrange the new numbers in descending (largest to smallest) order.
• We must identify which original number corresponds to the second largest transformed number.

Concept / Approach:
The important idea is that we cannot simply compare the original numbers, because the ordering decision is based on the modified numbers after swapping the first two digits. Therefore, we calculate the transformed value for each original number, pair each original with its transformed value, and then sort by the transformed values in descending order. The second highest transformed value corresponds to the required original number.

Step-by-Step Solution:
Step 1: Transform 376. Swapping the first two digits gives 736.Step 2: Transform 438. Swapping the first two digits gives 348.Step 3: Transform 476. Swapping the first two digits gives 746.Step 4: Transform 389. Swapping the first two digits gives 839.Step 5: Transform 567. Swapping the first two digits gives 657.Step 6: Now list the transformed numbers with their originals: 376 -> 736, 438 -> 348, 476 -> 746, 389 -> 839, 567 -> 657.Step 7: Arrange the transformed numbers in descending order: 839, 746, 736, 657, 348.Step 8: The highest transformed value is 839 from original 389; the second highest is 746 from original 476.

Verification / Alternative check:
We can recheck by quickly comparing the transformed values: 839 is clearly the largest three digit number among them, followed by 746, then 736, 657, and 348. Thus, there is no ambiguity about the second place. Carefully ensuring that each swap was carried out correctly prevents simple digit errors.

Why Other Options Are Wrong:
Option A (376) produces 736, which is the third largest transformed number, not the second. Option B (567) transforms to 657, which is only fourth in order. Option C (389) gives the largest transformed number 839, not the second largest. Therefore, these choices do not answer the question as asked.

Common Pitfalls:
A frequent mistake is to compare or sort the original numbers instead of the transformed ones, or to mis-swap digits like 476 into 467. Another pitfall is forgetting that the question asks for the original number in the second position, not the transformed one. Systematic calculation and clear pairing of original and transformed values help avoid errors.

Final Answer:
The original number whose transformed value is second in descending order is 476.